a bullet of mass m,with speed v,hits a fixed wooden block and penetrates a distance of l.find the average resistance of the wood.

To find the average resistance of the wood when a bullet of mass m, with speed v, penetrates a distance of l, we can use the concept of work.

The work done by the wood to stop the bullet is equal to the initial kinetic energy of the bullet. The work done (W) is given by the equation:

W = F * d

where F is the average resistance (force) of the wood and d is the distance penetrated by the bullet.

Now, the initial kinetic energy (KE) of the bullet is given by:

KE = (1/2) * m * v^2

Since the work done by the wood is equal to the initial kinetic energy of the bullet, we can equate the two equations:

W = KE

F * d = (1/2) * m * v^2

From this equation, we can solve for the average resistance (force) of the wood:

F = (1/2) * m * v^2 / d

So, the average resistance of the wood can be calculated by dividing half of the mass of the bullet multiplied by the square of its speed, by the distance penetrated by the bullet.